Question

On a certain "anticurl" operator

score 112 · Answer 1 · 2026-03-26 10:57:33

112

Views

On a certain "anticurl" operator

Published on 26 Mar 2026 - 10:57

score 26 · Answer 2 · 2026-03-26 10:58:06

26

Views

A vector field $V$ is gradient of some function $f$ on an open rectangular solid in $\mathbb{R}^3$

Published on 26 Mar 2026 - 10:58

score 300 · Answer 3 · 2026-03-26 11:04:48

300

Views

What is the vorticity of a velocity field?

Published on 26 Mar 2026 - 11:04

score 46 · Answer 4 · 2026-03-26 12:37:26

46

Views

How are the formal definitions of curl interpreted? Where do they appear from and how to derive them?

Published on 26 Mar 2026 - 12:37

score 33 · Answer 5 · 2026-04-14 04:21:33

33

Views

Dot product symbol for divergence, merely a convenience?

Published on 14 Apr 2026 - 4:21

score 121 · Answer 6 · 2026-04-15 14:43:35

121

Views

Why can the del operator cross product a triple integral be placed inside the triple integral?

Published on 15 Apr 2026 - 14:43

score 334 · Answer 7 · 2026-04-11 01:09:23

334

Views

Why is curl given by a cross product?

Published on 11 Apr 2026 - 1:09

score 92 · Answer 8 · 2026-03-26 11:05:28

92

Views

Stokes theorem applied to planes

Published on 26 Mar 2026 - 11:05

score 154 · Answer 9 · 2026-03-26 12:32:07

154

Views

Integration using Stokes' theorem

Published on 26 Mar 2026 - 12:32

score 126 · Answer 10 · 2026-03-26 11:05:10

126

Views

Find an irrotational function $F(x)$ and a solenoidal function $G(x)$ such that $H = F + G$.

Published on 26 Mar 2026 - 11:05

score 225 · Answer 11 · 2026-03-26 11:01:11

225

Views

Prove that $\bar{F} = r^n \bar{r}$ is conservative and find the scalar potential $\phi$ such that $F = grad\,\phi$.

Published on 26 Mar 2026 - 11:01

score 187 · Answer 12 · 2026-03-26 11:03:16

187

Views

If $\bar{F}=(xyz)^b (x^ai + y^aj + z^ak)$ be irrotational, then show that $b=0$ or $a=-1$. Find the scalar potential $\phi$.

Published on 26 Mar 2026 - 11:03

score 65 · Answer 13 · 2026-04-11 15:12:46

65

Views

If $\vec F=\frac{\vec r}{r^3}$ then $\exists$ is no $\vec G ∶ \mathbb{R}^3 ⧵ {0} \to \mathbb{R}^3$ such that $\vec F = curl \,\vec G$.

Published on 11 Apr 2026 - 15:12

score 25 · Answer 14 · 2026-03-26 11:00:51

25

Views

Is $(f_1(x)+f_2(y)+f_3(z))\vec{r}$ irrotational?

Published on 26 Mar 2026 - 11:00

score 68 · Answer 15 · 2026-03-26 12:38:04

68

Views

Show that $\nabla\cdot [(\vec u\times \vec v)\times \vec w]=\vec w\cdot [(\vec v\cdot \nabla)\vec u-(\vec u\cdot \nabla)\vec v]$

Published on 26 Mar 2026 - 12:38

List Question

On a certain "anticurl" operator

A vector field $V$ is gradient of some function $f$ on an open rectangular solid in $\mathbb{R}^3$

What is the vorticity of a velocity field?

How are the formal definitions of curl interpreted? Where do they appear from and how to derive them?

Dot product symbol for divergence, merely a convenience?

Why can the del operator cross product a triple integral be placed inside the triple integral?

Why is curl given by a cross product?

Stokes theorem applied to planes

Integration using Stokes' theorem

Find an irrotational function $F(x)$ and a solenoidal function $G(x)$ such that $H = F + G$.

Prove that $\bar{F} = r^n \bar{r}$ is conservative and find the scalar potential $\phi$ such that $F = grad\,\phi$.

If $\bar{F}=(xyz)^b (x^ai + y^aj + z^ak)$ be irrotational, then show that $b=0$ or $a=-1$. Find the scalar potential $\phi$.

If $\vec F=\frac{\vec r}{r^3}$ then $\exists$ is no $\vec G ∶ \mathbb{R}^3 ⧵ {0} \to \mathbb{R}^3$ such that $\vec F = curl \,\vec G$.

Is $(f_1(x)+f_2(y)+f_3(z))\vec{r}$ irrotational?

Show that $\nabla\cdot [(\vec u\times \vec v)\times \vec w]=\vec w\cdot [(\vec v\cdot \nabla)\vec u-(\vec u\cdot \nabla)\vec v]$

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